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Zeta integrals, Schwartz spaces and ...

Li, Wen-Wei.

Zeta integrals, Schwartz spaces and local functional equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Zeta integrals, Schwartz spaces and local functional equationsby Wen-Wei Li.
Author:	Li, Wen-Wei.
Published:	Cham :Springer International Publishing :2018.
Description:	viii, 141 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Functions, Zeta.
Online resource:	https://doi.org/10.1007/978-3-030-01288-5
ISBN:	9783030012885$q(electronic bk.)

Zeta integrals, Schwartz spaces and local functional equations
Li, Wen-Wei.

Zeta integrals, Schwartz spaces and local functional equations[electronic resource] /by Wen-Wei Li. - Cham :Springer International Publishing :2018. - viii, 141 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,22280075-8434 ;. - Lecture notes in mathematics ;2035..

Introduction -- Geometric Background -- Analytic Background -- Schwartz Spaces and Zeta Integrals -- Convergence of Some Zeta Integrals -- Prehomogeneous Vector Spaces -- The Doubling Method -- Speculation on the Global Integrals.

This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.

ISBN: 9783030012885$q(electronic bk.)

Standard No.: 10.1007/978-3-030-01288-5doiSubjects--Topical Terms:

239610
Functions, Zeta.

LC Class. No.: QA351 / .L594 2018

Dewey Class. No.: 515.56

Zeta integrals, Schwartz spaces and local functional equations
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245 1 0 $a Zeta integrals, Schwartz spaces and local functional equations $h [electronic resource] / $c by Wen-Wei Li.
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505 0 $a Introduction -- Geometric Background -- Analytic Background -- Schwartz Spaces and Zeta Integrals -- Convergence of Some Zeta Integrals -- Prehomogeneous Vector Spaces -- The Doubling Method -- Speculation on the Global Integrals.
520 $a This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.
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